What is the ruling on the prayer of someone who prayed Fajr only two rak'ahs, believing that it suffices for both Fajr and Subh prayers for years, and are his past prayers considered invalid?

If you intended these two rak'ahs as the obligatory prayer, then they suffice for you. And your intention of both "Salat al-Subh" and "Salat al-Fajr" simultaneously does not harm it, because they are two names for one prayer, with no difference between them. As for what you missed, it is the Sunnah of Fajr, which consists of two rak'ahs performed before the obligatory prayer.